Journal of Function Spaces http://www.hindawi.com The latest articles from Hindawi Publishing Corporation © 2015 , Hindawi Publishing Corporation . All rights reserved. On Noncompact Fractional Order Differential Inclusions with Generalized Boundary Condition and Impulses in a Banach Space Mon, 30 Mar 2015 13:52:16 +0000 http://www.hindawi.com/journals/jfs/2015/651359/ We provide existence results for a fractional differential inclusion with nonlocal conditions and impulses in a reflexive Banach space. We apply a technique based on weak topology to avoid any kind of compactness assumption on the nonlinear term. As an example we consider a problem in population dynamic described by an integro-partial-differential inclusion. Irene Benedetti, Valeri Obukhovskii, and Valentina Taddei Copyright © 2015 Irene Benedetti et al. All rights reserved. Variational Inequalities with Multivalued Lower Order Terms and Convex Functionals in Orlicz-Sobolev Spaces Wed, 25 Mar 2015 13:02:54 +0000 http://www.hindawi.com/journals/jfs/2015/321437/ We consider the existence of solutions of variational inequality form. Find , whose principal part is having a growth not necessarily of polynomial type, where is a second-order elliptic operator of Leray-Lions type, is a multivalued lower order term, and is a convex functional. We use subsupersolution methods to study the existence and enclosure of solutions in Orlicz-Sobolev spaces. Ge Dong and Xiaochun Fang Copyright © 2015 Ge Dong and Xiaochun Fang. All rights reserved. Three-Point Boundary Value Problems for Conformable Fractional Differential Equations Wed, 18 Mar 2015 15:40:13 +0000 http://www.hindawi.com/journals/jfs/2015/706383/ We study a fractional differential equation using a recent novel concept of fractional derivative with initial and three-point boundary conditions. We first obtain Green's function for the linear problem and then we study the nonlinear differential equation. H. Batarfi, Jorge Losada, Juan J. Nieto, and W. Shammakh Copyright © 2015 H. Batarfi et al. All rights reserved. New Set-Valued Integral in a Banach Space Mon, 16 Mar 2015 13:52:29 +0000 http://www.hindawi.com/journals/jfs/2015/260238/ We introduce and study a new set-valued integral of scalar-valued functions with respect to a set-valued measure in a Banach space. We investigate some properties and convergence theorems for this kind of integral. Cai-Li Zhou and Fu-Gui Shi Copyright © 2015 Cai-Li Zhou and Fu-Gui Shi. All rights reserved. On the Null Space Property of -Minimization for in Compressed Sensing Mon, 16 Mar 2015 10:03:16 +0000 http://www.hindawi.com/journals/jfs/2015/579853/ The paper discusses the relationship between the null space property (NSP) and the -minimization in compressed sensing. Several versions of the null space property, that is, the stable NSP, the robust NSP, and the robust NSP for based on the standard NSP, are proposed, and their equivalent forms are derived. Consequently, reconstruction results for the -minimization can be derived easily under the NSP condition and its equivalent form. Finally, the NSP is extended to the -synthesis modeling and the mixed -minimization, which deals with the dictionary-based sparse signals and the block sparse signals, respectively. Yi Gao, Jigen Peng, Shigang Yue, and Yuan Zhao Copyright © 2015 Yi Gao et al. All rights reserved. A Subordination Principle on Wright Functions and Regularized Resolvent Families Mon, 16 Mar 2015 06:53:25 +0000 http://www.hindawi.com/journals/jfs/2015/158145/ We obtain a vector-valued subordination principle for -regularized resolvent families which unified and improves various previous results in the literature. As a consequence, we establish new relations between solutions of different fractional Cauchy problems. To do that, we consider scaled Wright functions which are related to Mittag-Leffler functions, the fractional calculus, and stable Lévy processes. We study some interesting properties of these functions such as subordination (in the sense of Bochner), convolution properties, and their Laplace transforms. Finally we present some examples where we apply these results. Luciano Abadias and Pedro J. Miana Copyright © 2015 Luciano Abadias and Pedro J. Miana. All rights reserved. Space of -Periodic Limit Functions and Its Applications to an Abstract Cauchy Problem Sun, 15 Mar 2015 07:05:47 +0000 http://www.hindawi.com/journals/jfs/2015/953540/ We introduce a new space consisting of what we call -periodic limit functions. We investigate some properties of the new function space. In particular, we study inclusion relations among asymptotically periodic type function spaces. Finally, we apply the -periodic limit functions to investigate the existence and uniqueness of asymptotically -periodic mild solutions of an abstract Cauchy problem. Rui Xie and Chuanyi Zhang Copyright © 2015 Rui Xie and Chuanyi Zhang. All rights reserved. Toeplitz Operators on the Weighted Bergman Space over the Two-Dimensional Unit Ball Wed, 11 Mar 2015 10:52:23 +0000 http://www.hindawi.com/journals/jfs/2015/306168/ We extend the known results on commutative Banach algebras generated by Toeplitz operators with radial quasi-homogeneous symbols on the two-dimensional unit ball. Spherical coordinates previously used hid a possibility to detect an essentially wider class of symbols that can generate commutative Banach Toeplitz operator algebras. We characterize these new algebras describing their properties and, under a certain extra condition, construct the corresponding Gelfand theory. Alma García and Nikolai Vasilevski Copyright © 2015 Alma García and Nikolai Vasilevski. All rights reserved. A Reverse Theorem on the - Continuity of the Dual Map Tue, 10 Mar 2015 09:12:39 +0000 http://www.hindawi.com/journals/jfs/2015/864173/ Given a Banach space , , and , we define the set of all for which there exist two sequences and such that converges to , has a subnet -convergent to , and for all . We prove that if is separable and reflexive and enjoys the Radon-Riesz property, then is contained in the boundary of relative to . We also show that if is infinite dimensional and separable, then there exists an equivalent norm on such that the interior of relative to is contained in . Mienie de Kock and Francisco Javier García-Pacheco Copyright © 2015 Mienie de Kock and Francisco Javier García-Pacheco. All rights reserved. The Singular Points of Analytic Functions with Finite -Order Defined by Laplace-Stieltjes Transformations Mon, 02 Mar 2015 06:54:36 +0000 http://www.hindawi.com/journals/jfs/2015/865069/ We study the singular points of analytic functions defined by Laplace-Stieltjes transformations which converge on the right half plane, by introducing the concept of -order functions. We also confirm the existence of the finite -order Borel points of such functions and obtained the extension of the finite -order Borel point of two analytic functions defined by two Laplace-Stieltjes transformations convergent on the right half plane. The main results of this paper are improvement of some theorems given by Shang and Gao. Hong-Yan Xu and Zu-Xing Xuan Copyright © 2015 Hong-Yan Xu and Zu-Xing Xuan. All rights reserved. Jordan Type Inequalities for Hyperbolic Functions and Their Applications Sun, 01 Mar 2015 14:16:04 +0000 http://www.hindawi.com/journals/jfs/2015/370979/ We present the best possible parameters p, such that the double inequality holds for all . As applications, some new inequalities for certain special function and bivariate means are found. Zhen-Hang Yang and Yu-Ming Chu Copyright © 2015 Zhen-Hang Yang and Yu-Ming Chu. All rights reserved. Existence and Asymptotic Behaviour of Solutions of Differential and Integral Equations in Some Function Spaces Sun, 01 Mar 2015 10:25:40 +0000 http://www.hindawi.com/journals/jfs/2015/235043/ Józef Banaś, Mohamed Abdalla Darwish, Leszek Olszowy, and Kishin Sadarangani Copyright © 2015 Józef Banaś et al. All rights reserved. Some Basic Properties of Certain New Subclass of Meromorphic Functions Sun, 01 Mar 2015 08:03:31 +0000 http://www.hindawi.com/journals/jfs/2015/196060/ We introduce and investigate a new subclass of meromorphic functions. Some interesting properties such as inclusion relationship, coefficient estimates, neighborhoods, and partial sums are proved. Connections of the results with known results are also considered. Lei Shi and Zhi-Gang Wang Copyright © 2015 Lei Shi and Zhi-Gang Wang. All rights reserved. Fixed Points of Modified -Contractive Mappings in Complete Metric-Like Spaces Sat, 28 Feb 2015 09:48:32 +0000 http://www.hindawi.com/journals/jfs/2015/270971/ We introduce the notion of modified -contractive mappings in the setting of complete metric-like spaces and we investigate the existence and uniqueness of fixed point of such mappings. The presented results unify, extend, and improve several results in the related literature. Hamed H. Alsulami, Erdal Karapınar, and Hossein Piri Copyright © 2015 Hamed H. Alsulami et al. All rights reserved. Coefficient Estimates for Two New Subclasses of Biunivalent Functions with respect to Symmetric Points Wed, 25 Feb 2015 08:33:12 +0000 http://www.hindawi.com/journals/jfs/2015/145242/ We introduce two subclasses of biunivalent functions and find estimates on the coefficients and for functions in these new subclasses. Also, consequences of the results are pointed out. Şahsene Altınkaya and Sibel Yalçın Copyright © 2015 Şahsene Altınkaya and Sibel Yalçın. All rights reserved. Picard Sequence and Fixed Point Results on -Metric Spaces Wed, 25 Feb 2015 07:06:24 +0000 http://www.hindawi.com/journals/jfs/2015/189861/ We obtain some fixed point results for single-valued and multivalued mappings in the setting of a -metric space. These results are generalizations of the analogous ones recently proved by Khojasteh, Abbas, and Costache. Marta Demma and Pasquale Vetro Copyright © 2015 Marta Demma and Pasquale Vetro. All rights reserved. A New Characterization of -Uniformly Rotund Banach Space Tue, 24 Feb 2015 14:19:03 +0000 http://www.hindawi.com/journals/jfs/2015/865305/ A new characterization of -uniformly rotund Banach space with is given. Moreover, a corresponding result in the locally -uniformly rotund Banach space with is given. Suyalatu Wulede, Tingting Li, and Xuan Qin Copyright © 2015 Suyalatu Wulede et al. All rights reserved. Continuous Dependence of the Solutions of Nonlinear Integral Quadratic Volterra Equation on the Parameter Mon, 23 Feb 2015 08:07:24 +0000 http://www.hindawi.com/journals/jfs/2015/471235/ We prove results on the existence and continuous dependence of solutions of a nonlinear quadratic integral Volterra equation on a parameter. This dependence is investigated in terms of Hausdorff distance. The considerations are placed in the Banach space and the Fréchet space. Szymon Dudek and Leszek Olszowy Copyright © 2015 Szymon Dudek and Leszek Olszowy. All rights reserved. Inequalities Characterizing Linear-Multiplicative Functionals Mon, 23 Feb 2015 07:47:02 +0000 http://www.hindawi.com/journals/jfs/2015/945758/ We prove, in an elementary way, that if a nonconstant real-valued mapping defined on a real algebra with a unit satisfies certain inequalities, then it is a linear and multiplicative functional. Moreover, we determine all Jensen concave and supermultiplicative operators , where and are compact Hausdorff spaces. Włodzimierz Fechner Copyright © 2015 Włodzimierz Fechner. All rights reserved. The Generalized Green’s Function for Boundary Value Problem of Second Order Difference Equation Mon, 23 Feb 2015 06:37:20 +0000 http://www.hindawi.com/journals/jfs/2015/201946/ Let and . In this paper, by building the generalized Green’s function for the problems, we study the solvability of the S-L problem , , , and the periodic S-L problem , , where the parameter is an eigenvalue of the linear problem , , or the problem , , and , is defined and real valued on , and in the periodic S-L problem we have . Xiaoling Han and Juanjuan Huang Copyright © 2015 Xiaoling Han and Juanjuan Huang. All rights reserved. Some Classes of Continuous Operators on Spaces of Bounded Vector-Valued Continuous Functions with the Strict Topology Sun, 22 Feb 2015 14:39:14 +0000 http://www.hindawi.com/journals/jfs/2015/796753/ Let be a completely regular Hausdorff space and let and be Banach spaces. Let be the space of all -valued bounded, continuous functions on , equipped with the strict topology . We study the relationship between important classes of -continuous linear operators (strongly bounded, unconditionally converging, weakly completely continuous, completely continuous, weakly compact, nuclear, and strictly singular) and the corresponding operator measures given by Riesz representing theorems. Some applications concerning the coincidence among these classes of operators are derived. Marian Nowak Copyright © 2015 Marian Nowak. All rights reserved. Some Results for Periodic Solutions of a Kind of Liénard Equation Sun, 22 Feb 2015 06:58:53 +0000 http://www.hindawi.com/journals/jfs/2015/519747/ We investigate the following Liénard-type -Laplacian equation with a deviating argument . Some new criteria for guaranteeing the existence and uniqueness of periodic solutions of this equation are given by using the Manásevich-Mawhin continuation theorem and some analysis techniques. Our results hold under weaker conditions than some known results from the literature and are more effective. In the last section, an illustrative example is provided to demonstrate the applications of the theoretical results. Yong Wang and Xiangyi Yi Copyright © 2015 Yong Wang and Xiangyi Yi. All rights reserved. On Traces in Some Analytic Spaces in Bounded Strictly Pseudoconvex Domains Thu, 19 Feb 2015 10:34:05 +0000 http://www.hindawi.com/journals/jfs/2015/265245/ New sharp estimates of traces of Bergman type spaces of analytic functions in bounded strictly pseudoconvex domains are obtained. These are, as far as we know, the first results of this type which are valid for any bounded strictly pseudoconvex domains with smooth boundary. Romi F. Shamoyan and Olivera R. Mihić Copyright © 2015 Romi F. Shamoyan and Olivera R. Mihić. All rights reserved. A General Uniqueness Theorem concerning the Stability of Additive and Quadratic Functional Equations Tue, 17 Feb 2015 08:22:06 +0000 http://www.hindawi.com/journals/jfs/2015/643969/ We prove a general uniqueness theorem that can be easily applied to the (generalized) Hyers-Ulam stability of the Cauchy additive functional equation, the quadratic functional equation, and the quadratic-additive type functional equations. This uniqueness theorem can replace the repeated proofs for uniqueness of the relevant solutions of given equations while we investigate the stability of functional equations. Yang-Hi Lee and Soon-Mo Jung Copyright © 2015 Yang-Hi Lee and Soon-Mo Jung. All rights reserved. Volterra Type Integral Operators and Composition Operators on Model Spaces Thu, 12 Feb 2015 13:08:30 +0000 http://www.hindawi.com/journals/jfs/2015/467802/ We study some mapping properties of Volterra type integral operators and composition operators on model spaces. We also discuss and give out a couple of interesting open problems in model spaces where any possible solution of the problems can be used to study a number of other operator theoretic related problems in the spaces. Tesfa Mengestie Copyright © 2015 Tesfa Mengestie. All rights reserved. Ulam Problem for the Cosine Addition Formula in Sato Hyperfunctions Thu, 12 Feb 2015 09:49:38 +0000 http://www.hindawi.com/journals/jfs/2015/615167/ We prove the Ulam problem for the cosine addition formula in the spaces of Schwartz distributions and Sato hyperfunctions with respect to bounded distributions and bounded hyperfunctions. Jaeyoung Chung and Soon-Yeong Chung Copyright © 2015 Jaeyoung Chung and Soon-Yeong Chung. All rights reserved. Large Function Algebras with Certain Topological Properties Tue, 10 Feb 2015 12:55:42 +0000 http://www.hindawi.com/journals/jfs/2015/761924/ Let be a family of continuous functions defined on a compact interval. We give a sufficient condition so that contains a dense -generated free algebra; in other words, is densely -strongly algebrable. As an application we obtain dense -strong algebrability of families of nowhere Hölder functions, Bruckner-Garg functions, functions with a dense set of local maxima and local minima, and nowhere monotonous functions differentiable at all but finitely many points. We also study the problem of the existence of large closed algebras within where or . We prove that the set of perfectly everywhere surjective functions together with the zero function contains a -generated algebra closed in the topology of uniform convergence while it does not contain a nontrivial algebra closed in the pointwise convergence topology. We prove that an infinitely generated algebra which is closed in the pointwise convergence topology needs to contain two valued functions and infinitely valued functions. We give an example of such an algebra; namely, it was shown that there is a subalgebra of with generators which is closed in the pointwise topology and, for any function in this algebra, there is an open set such that is a Bernstein set. Artur Bartoszewicz and Szymon Głąb Copyright © 2015 Artur Bartoszewicz and Szymon Głąb. All rights reserved. Representation of Group Isomorphisms: The Compact Case Tue, 03 Feb 2015 08:54:51 +0000 http://www.hindawi.com/journals/jfs/2015/879414/ Let be a discrete group and let and be two subgroups of -valued continuous functions defined on two 0-dimensional compact spaces and . A group isomorphism defined between and is called separating when, for each pair of maps satisfying that , it holds that . We prove that under some mild conditions every biseparating isomorphism can be represented by means of a continuous function as a weighted composition operator. As a consequence we establish the equivalence of two subgroups of continuous functions if there is a biseparating isomorphism defined between them. Marita Ferrer, Margarita Gary, and Salvador Hernández Copyright © 2015 Marita Ferrer et al. All rights reserved. Korovkin-Type Theorems for Modular --Statistical Convergence Sat, 31 Jan 2015 13:22:48 +0000 http://www.hindawi.com/journals/jfs/2015/160401/ We deal with a new type of statistical convergence for double sequences, called --statistical convergence, and we prove a Korovkin-type approximation theorem with respect to this type of convergence in modular spaces. Finally, we give some application to moment-type operators in Orlicz spaces. Carlo Bardaro, Antonio Boccuto, Kamil Demirci, Ilaria Mantellini, and Sevda Orhan Copyright © 2015 Carlo Bardaro et al. All rights reserved. Tricorns and Multicorns of -Iteration Scheme Wed, 28 Jan 2015 12:03:57 +0000 http://www.hindawi.com/journals/jfs/2015/417167/ Complex graphics of dynamical system have striking features of fractals and become a wide area of research due to their beauty and complexity of their nature. The aim of this paper is to study dynamics of relative superior tricorns and multicorns using -iteration schemes. Several examples are presented to explore the geometry of relative superior tricorns and multicorns for antipolynomial of complex polynomial for . Shin Min Kang, Arif Rafiq, Abdul Latif, Abdul Aziz Shahid, and Young Chel Kwun Copyright © 2015 Shin Min Kang et al. All rights reserved.